My search-fu has failed, so I'll just ask:
1: Does a weapon's hardness apply verses the gray slime?
2: If using the ghost touch arrows as improvised melee weapons on one of the incorporeals, do both the improvised weapon and wrong sized weapon penalties apply?
1. Pretty sure it does not
2. Improvised weapon penalty only. Wrong size weapon penalties are for weapons that are larger than you can handle in 2 hands or smaller than you can hold in one and arrows are neither of those for medium and small races. Now, a small arrow used by a large creature would probably be both.
Thanks, MurphysParadox.